In your own words, explain how to solve a quadratic equation by completing the square. Demonstrate the process with your own example.
answer with 150 to 200 words

Question

anonymous · Answer

Quadratic form ax^2+bx+c

Complete the square - f(x) = -2x^2+4x+1 
 - separate the variables 
     -2x^2+4x+1=0
     -2x^2+4x=-1
 - ensure a = 1
   -2x^2+4x=-1/-2 = x^2-2x=1/2
 - find b/2
   -2/2 = -1
 - add (b/2)^2 to both sides

  (-2/2)^2 = 1
   x^2-2x+1 = 1/2 +1
 - variable side of the equation becomes the square of a binomial (x+b/2a)^2
  
   x^2-2x +1 = (x-1)^2
 
 - solve for x
$$\sqrt{(x-1)^2} = \pm \sqrt{3/2}$$

$$x-1 = \pm \sqrt{3/2}$$

$$x = \pm \sqrt{3/2} +1$$

$$x = 1 + \pm \sqrt{3/2}$$ 

$$x = 1 \sqrt{3}/\sqrt{2} * \sqrt{2}/\sqrt{2}$$

$$x = 1 \pm \sqrt{6}/2 $$